1. Field of the Invention
The present invention relates to a digital filter and its designing method and is particularly suitable for an FIR filter, which comprises a tapped delay line made up of a plurality of delay units and performs addition and output after multiplying the signals of taps by several times.
2. Description of the Related Art
Some kind of digital signal processing is generally performed in various kinds of electronic devices provided in different fields of communication, measurement, sound/image signal processing, medical care, seismology, and so on. The most significant basic operation of the digital signal processing is filtering which extracts only a signal having a necessary frequency band from mixed input signals of various signals and noise. Thus, digital filters are frequently used in electronic devices for performing digital signal processing.
An IIR (Infinite Impulse Response) filter and an FIR (Finite Impulse Response) filter are frequently used as a digital filter. The FIR filter has the following advantages: first, since the transfer factor of the FIR filter has a pole only on the origin of the z-plane, a circuit is always stable, and second, linear phase characteristics are achieved with complete accuracy.
When filters are classified based on the arrangement of a pass band and a stop band, filters are divided into four of a low-pass filter, a high-pass filter, a bandpass filter, and a band-stop filter. The low-pass filter is basically used for the IIR filter and the FIR filter. The other high-pass filter, bandpass filter, and band-stop filter are derived from the low-pass filter by performing processing such as frequency conversion.
In some applications of electronic devices, symmetrical FIR filters are used. The symmetrical FIR filter is composed of a pair of a low-pass filter and a high-pass filter that have symmetrical frequency characteristics. In such a symmetrical FIR filter, a basic low-pass filter is first designed and frequency conversion is performed thereon, so that a high-pass filter is designed with characteristics symmetrical to those of the low-pass filter.
Incidentally in the FIR filter, an impulse response represented by a finite time length acts as a filter factor as it is. Therefore, designing the FIR filter is to determine filter factors to obtain desired frequency characteristics.
Conventionally in frequency conversion for deriving filter factors of a high-pass filter and so forth from an FIR low-pass filter, the cut-off frequency of the filter is converted. To be specific, convolution or the like using a window function, Chebyshev approximation, and so forth is performed based on a ratio of a sampling frequency and a cut-off frequency, so that the transfer factor of the filter is determined. The transfer factor is further converted into a frequency component.
However, in the frequency conversion using a window function, Chebyshev approximation, and so forth, calculation is extremely complicated. Thus, calculation performed by software increases a processing load and calculation performed by hardware increases a circuit size.
Further, the frequency characteristics of a filter that are obtained by conventional design methods depend upon a window function and approximation. Thus, when the window function and approximation are not properly set, excellent frequency characteristics cannot be obtained. However, it is generally difficult to properly set a window function and approximation and thus it is quite demanding to design a filter with desired frequency characteristics.
Moreover, a method of directly determining a filter factor of a high-pass filter and so forth regardless of frequency conversion is also available. However, in this case, filter factors required for desired frequency characteristics have to be determined by trial and error, so that a design cannot be made with ease.
The present invention is devised to solve the above-described problems. An object of the present invention is to readily design an FIR digital filter having desired frequency characteristics.